0123_0132_0321_1320_3021
Counting sequence:
1, 1, 2, 6, 19, 54, 143, 363, 901, 2219, 5475, 13602, 34084, 86121, 219172, 561051, 1442904, 3724444, 9641351, 25015325, 65022509, 169259009, 441107591, 1150645276, 3003737284, 7845870599, 20503446608, 53601531693, 140171097776, 366643294034, 959205098555, 2509831107127, 6567939361869, 17189155081871, 44989593704947, 117759224861966, 308246204863084, 806893490283229, 2112258172216836, 5529520248990135, 14475563840239504, 37895659443084864, 99208322112389111, 259722984702030921, 679947712731864949, 1780093765214262869, 4660279706840904423, 12200635404145389048, 31941402205222885276, 83623113814685771499, 218927006852973703360, 573156006788142136377, 1500537143230522493304, 3928447541604076966246, 10284789437508035378747, 26925888119822730171731, 70492808493865650813989, 184552402253785400499539, 483164123547913280377571, 1264939409943600645930970, 3311652971375782559232724, 8670017198340737817195569, 22698393939902818426097156, 59425155109765304453600691, 155577052077957892768940264, 407305961924777217219271364, 1066340754144789941015203463, 2791716139100581960866452053, 7308807335727248633238215901, 19134705203998377285302852489, 50095306929655565841871495015, 131151212854850197331296316852, 343358326100871804039150191764, 898923754232144817970744989871, 2353412913869173951062915189072, 6161314941332303827238957629221, 16130531816860999493978462491744, 42230280320356035339910618934874, 110560308761695421413312129507931, 289450645190262125709403951909455, 757791625241265283402177512496669, 1983924227360103448008726999050999, 5193981050416626643921285990948851, 13598018910893823922897867342462086, 35600075655970708548154131483168604, 93202208003825565658520843416388709, 244006548247911590481706402213384228, 638817436522302558255965111772701583, 1672445760878947085946463913507527776, 4378519845224769296347059556161790504, 11463113772996479183508146543010499895, 30010821470128219388776575515348762177, 78569350630037909999564634620817243749, 205697230405130230138492765048308254621, 538522340555332734463243188857798295047, 1409869791200208911326253168055023833936, 3691087032922737935626263668092253943724, 9663391307320416887695461781241906923859, 25299086888538384951588828044574214140416, 66233869357284578895014152048163043348465, 173402521181275226548711321406881152111464
Generating function in Maple syntax:
-(x^11+3*x^10-28*x^9+55*x^8-87*x^7+151*x^6-221*x^5+219*x^4-137*x^3+52*x^2-11*x+1)/(x^2-3*x+1)/(2*x-1)^2/(-1+x)^5
Generating function in latex syntax:
-\frac{x^{11}+3 x^{10}-28 x^{9}+55 x^{8}-87 x^{7}+151 x^{6}-221 x^{5}+219 x^{4}-137 x^{3}+52 x^{2}-11 x +1}{\left(x^{2}-3 x +1\right) \left(2 x -1\right)^{2} \left(-1+x \right)^{5}}
Generating function in sympy syntax:
(-x**11 - 3*x**10 + 28*x**9 - 55*x**8 + 87*x**7 - 151*x**6 + 221*x**5 - 219*x**4 + 137*x**3 - 52*x**2 + 11*x - 1)/((x - 1)**5*(2*x - 1)**2*(x**2 - 3*x + 1))
Implicit equation for the generating function in Maple syntax:
(x^2-3*x+1)*(2*x-1)^2*(-1+x)^5*F(x)+x^11+3*x^10-28*x^9+55*x^8-87*x^7+151*x^6-221*x^5+219*x^4-137*x^3+52*x^2-11*x+1 = 0
Implicit equation for the generating function in latex syntax:
\left(x^{2}-3 x +1\right) \left(2 x -1\right)^{2} \left(-1+x \right)^{5} F \! \left(x \right)+x^{11}+3 x^{10}-28 x^{9}+55 x^{8}-87 x^{7}+151 x^{6}-221 x^{5}+219 x^{4}-137 x^{3}+52 x^{2}-11 x +1 = 0
Explicit closed form in Maple syntax:
piecewise(Or(n = 0,n = 1),1,n = 2,2,1/240*(-24*5^(1/2)+120)*(3/2-1/2*5^(1/2))^(-n)+1/240*(24*5^(1/2)+120)*(3/2+1/2*5^(1/2))^(-n)+1/240*(15*n+105)*2^n+1/12*n^4-n^3+59/12*n^2-13*n+11)
Explicit closed form in latex syntax:
\left\{\begin{array}{cc}1 & n =0\text{ or } n =1 \\ 2 & n =2 \\ \frac{\left(-24 \sqrt{5}+120\right) \left(\frac{3}{2}-\frac{\sqrt{5}}{2}\right)^{-n}}{240}+\frac{\left(24 \sqrt{5}+120\right) \left(\frac{3}{2}+\frac{\sqrt{5}}{2}\right)^{-n}}{240}+\\\frac{\left(15 n +105\right) 2^{n}}{240}+\frac{n^{4}}{12}-n^{3}+\frac{59 n^{2}}{12}-13 n +11 & \mathit{\text{otherwise}} \end{array}\right.
Recurrence in maple format:
a(0) = 1
a(1) = 1
a(2) = 2
a(3) = 6
a(4) = 19
a(5) = 54
a(6) = 143
a(7) = 363
a(8) = 901
a(9) = 2219
a(10) = 5475
a(11) = 13602
a(n+4) = -4*a(n)+16*a(n+1)-17*a(n+2)+7*a(n+3)-1/12*(n-3)*(n^3-13*n^2+26*n+4), n >= 12
Recurrence in latex format:
a \! \left(0\right) = 1
a \! \left(1\right) = 1
a \! \left(2\right) = 2
a \! \left(3\right) = 6
a \! \left(4\right) = 19
a \! \left(5\right) = 54
a \! \left(6\right) = 143
a \! \left(7\right) = 363
a \! \left(8\right) = 901
a \! \left(9\right) = 2219
a \! \left(10\right) = 5475
a \! \left(11\right) = 13602
a \! \left(n +4\right) = -4 a \! \left(n \right)+16 a \! \left(n +1\right)-17 a \! \left(n +2\right)+7 a \! \left(n +3\right)-\frac{\left(n -3\right) \left(n^{3}-13 n^{2}+26 n +4\right)}{12}, \quad n \geq 12
Specification 1
Strategy pack name: point_placements
Tree: http://permpal.com/tree/16274/
System of equations in Maple syntax:
F[0,x] = F[1,x]+F[2,x]
F[1,x] = 1
F[2,x] = F[3,x]
F[3,x] = F[4,x]*F[5,x]
F[4,x] = x
F[5,x] = F[19,x]+F[6,x]
F[6,x] = F[1,x]+F[7,x]
F[7,x] = F[8,x]
F[8,x] = F[4,x]*F[9,x]
F[9,x] = F[10,x]+F[11,x]
F[10,x] = F[1,x]+F[4,x]
F[11,x] = F[12,x]+F[14,x]
F[12,x] = F[13,x]
F[13,x] = F[10,x]*F[4,x]
F[14,x] = F[15,x]+F[16,x]+F[18,x]
F[15,x] = 0
F[16,x] = F[17,x]*F[4,x]
F[17,x] = F[4,x]
F[18,x] = F[12,x]*F[4,x]
F[19,x] = F[20,x]+F[52,x]
F[20,x] = F[21,x]
F[21,x] = F[22,x]*F[4,x]
F[22,x] = F[23,x]+F[24,x]
F[23,x] = F[1,x]+F[12,x]
F[24,x] = F[20,x]+F[25,x]
F[25,x] = F[15,x]+F[26,x]+F[50,x]
F[26,x] = F[27,x]*F[4,x]
F[27,x] = F[28,x]+F[30,x]
F[28,x] = F[12,x]+F[29,x]
F[29,x] = F[16,x]
F[30,x] = F[25,x]+F[31,x]
F[31,x] = 2*F[15,x]+F[32,x]+F[36,x]
F[32,x] = F[33,x]*F[4,x]
F[33,x] = F[34,x]+F[35,x]
F[34,x] = F[29,x]
F[35,x] = F[31,x]
F[36,x] = F[37,x]*F[4,x]
F[37,x] = F[38,x]
F[38,x] = F[15,x]+F[39,x]+F[49,x]
F[39,x] = F[4,x]*F[40,x]
F[40,x] = F[41,x]+F[43,x]
F[41,x] = F[4,x]+F[42,x]
F[42,x] = F[16,x]
F[43,x] = F[38,x]+F[44,x]
F[44,x] = 2*F[15,x]+F[36,x]+F[45,x]
F[45,x] = F[4,x]*F[46,x]
F[46,x] = F[47,x]+F[48,x]
F[47,x] = F[42,x]
F[48,x] = F[44,x]
F[49,x] = F[20,x]*F[4,x]
F[50,x] = F[4,x]*F[51,x]
F[51,x] = F[20,x]+F[38,x]
F[52,x] = F[137,x]+F[15,x]+F[53,x]
F[53,x] = F[4,x]*F[54,x]
F[54,x] = F[55,x]+F[62,x]
F[55,x] = F[56,x]+F[7,x]
F[56,x] = F[15,x]+F[16,x]+F[57,x]
F[57,x] = F[4,x]*F[58,x]
F[58,x] = F[11,x]+F[59,x]
F[59,x] = F[29,x]+F[60,x]
F[60,x] = F[61,x]
F[61,x] = F[29,x]*F[4,x]
F[62,x] = F[52,x]+F[63,x]
F[63,x] = F[125,x]+F[15,x]+F[64,x]+F[90,x]
F[64,x] = F[4,x]*F[65,x]
F[65,x] = F[66,x]+F[70,x]
F[66,x] = F[56,x]+F[67,x]
F[67,x] = F[68,x]
F[68,x] = F[4,x]*F[69,x]
F[69,x] = F[59,x]
F[70,x] = F[63,x]+F[71,x]
F[71,x] = 2*F[15,x]+F[72,x]+F[76,x]+F[77,x]
F[72,x] = F[4,x]*F[73,x]
F[73,x] = F[74,x]+F[75,x]
F[74,x] = F[67,x]
F[75,x] = F[71,x]
F[76,x] = 0
F[77,x] = F[4,x]*F[78,x]
F[78,x] = F[79,x]
F[79,x] = F[80,x]+F[84,x]
F[80,x] = F[81,x]
F[81,x] = F[4,x]*F[82,x]
F[82,x] = F[34,x]+F[83,x]
F[83,x] = F[80,x]
F[84,x] = 3*F[15,x]+F[85,x]+F[89,x]
F[85,x] = F[4,x]*F[86,x]
F[86,x] = F[87,x]+F[88,x]
F[87,x] = F[60,x]
F[88,x] = F[84,x]
F[89,x] = F[4,x]*F[80,x]
F[90,x] = F[4,x]*F[91,x]
F[91,x] = F[92,x]
F[92,x] = F[15,x]+F[49,x]+F[93,x]
F[93,x] = F[4,x]*F[94,x]
F[94,x] = F[95,x]+F[96,x]
F[95,x] = F[14,x]+F[4,x]
F[96,x] = F[92,x]+F[97,x]
F[97,x] = F[106,x]+F[15,x]+F[90,x]+F[98,x]
F[98,x] = F[4,x]*F[99,x]
F[99,x] = F[100,x]+F[101,x]
F[100,x] = F[14,x]+F[60,x]
F[101,x] = F[102,x]+F[97,x]
F[102,x] = 2*F[15,x]+F[103,x]+F[76,x]+F[89,x]
F[103,x] = F[104,x]*F[4,x]
F[104,x] = F[105,x]+F[87,x]
F[105,x] = F[102,x]
F[106,x] = F[107,x]*F[4,x]
F[107,x] = F[108,x]
F[108,x] = F[109,x]*F[4,x]
F[109,x] = F[110,x]+F[28,x]
F[110,x] = F[107,x]+F[111,x]
F[111,x] = 2*F[15,x]+F[112,x]+F[115,x]
F[112,x] = F[113,x]*F[4,x]
F[113,x] = F[114,x]+F[34,x]
F[114,x] = F[111,x]
F[115,x] = F[116,x]*F[4,x]
F[116,x] = F[117,x]
F[117,x] = F[118,x]
F[118,x] = F[119,x]*F[4,x]
F[119,x] = F[120,x]+F[41,x]
F[120,x] = F[117,x]+F[121,x]
F[121,x] = 2*F[15,x]+F[115,x]+F[122,x]
F[122,x] = F[123,x]*F[4,x]
F[123,x] = F[124,x]+F[47,x]
F[124,x] = F[121,x]
F[125,x] = F[126,x]*F[4,x]
F[126,x] = F[127,x]+F[79,x]
F[127,x] = F[107,x]+F[128,x]
F[128,x] = 2*F[15,x]+F[106,x]+F[129,x]
F[129,x] = F[130,x]*F[4,x]
F[130,x] = F[100,x]+F[131,x]
F[131,x] = F[128,x]+F[132,x]
F[132,x] = 2*F[15,x]+F[133,x]+F[136,x]+F[89,x]
F[133,x] = F[134,x]*F[4,x]
F[134,x] = F[135,x]+F[87,x]
F[135,x] = F[132,x]
F[136,x] = 0
F[137,x] = F[138,x]*F[4,x]
F[138,x] = F[127,x]+F[139,x]
F[139,x] = F[20,x]+F[92,x]
System of equations in latex syntax:
F_{0}\! \left(x \right) = F_{1}\! \left(x \right)+F_{2}\! \left(x \right)
F_{1}\! \left(x \right) = 1
F_{2}\! \left(x \right) = F_{3}\! \left(x \right)
F_{3}\! \left(x \right) = F_{4}\! \left(x \right) F_{5}\! \left(x \right)
F_{4}\! \left(x \right) = x
F_{5}\! \left(x \right) = F_{19}\! \left(x \right)+F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{1}\! \left(x \right)+F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{4}\! \left(x \right) F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{10}\! \left(x \right)+F_{11}\! \left(x \right)
F_{10}\! \left(x \right) = F_{1}\! \left(x \right)+F_{4}\! \left(x \right)
F_{11}\! \left(x \right) = F_{12}\! \left(x \right)+F_{14}\! \left(x \right)
F_{12}\! \left(x \right) = F_{13}\! \left(x \right)
F_{13}\! \left(x \right) = F_{10}\! \left(x \right) F_{4}\! \left(x \right)
F_{14}\! \left(x \right) = F_{15}\! \left(x \right)+F_{16}\! \left(x \right)+F_{18}\! \left(x \right)
F_{15}\! \left(x \right) = 0
F_{16}\! \left(x \right) = F_{17}\! \left(x \right) F_{4}\! \left(x \right)
F_{17}\! \left(x \right) = F_{4}\! \left(x \right)
F_{18}\! \left(x \right) = F_{12}\! \left(x \right) F_{4}\! \left(x \right)
F_{19}\! \left(x \right) = F_{20}\! \left(x \right)+F_{52}\! \left(x \right)
F_{20}\! \left(x \right) = F_{21}\! \left(x \right)
F_{21}\! \left(x \right) = F_{22}\! \left(x \right) F_{4}\! \left(x \right)
F_{22}\! \left(x \right) = F_{23}\! \left(x \right)+F_{24}\! \left(x \right)
F_{23}\! \left(x \right) = F_{1}\! \left(x \right)+F_{12}\! \left(x \right)
F_{24}\! \left(x \right) = F_{20}\! \left(x \right)+F_{25}\! \left(x \right)
F_{25}\! \left(x \right) = F_{15}\! \left(x \right)+F_{26}\! \left(x \right)+F_{50}\! \left(x \right)
F_{26}\! \left(x \right) = F_{27}\! \left(x \right) F_{4}\! \left(x \right)
F_{27}\! \left(x \right) = F_{28}\! \left(x \right)+F_{30}\! \left(x \right)
F_{28}\! \left(x \right) = F_{12}\! \left(x \right)+F_{29}\! \left(x \right)
F_{29}\! \left(x \right) = F_{16}\! \left(x \right)
F_{30}\! \left(x \right) = F_{25}\! \left(x \right)+F_{31}\! \left(x \right)
F_{31}\! \left(x \right) = 2 F_{15}\! \left(x \right)+F_{32}\! \left(x \right)+F_{36}\! \left(x \right)
F_{32}\! \left(x \right) = F_{33}\! \left(x \right) F_{4}\! \left(x \right)
F_{33}\! \left(x \right) = F_{34}\! \left(x \right)+F_{35}\! \left(x \right)
F_{34}\! \left(x \right) = F_{29}\! \left(x \right)
F_{35}\! \left(x \right) = F_{31}\! \left(x \right)
F_{36}\! \left(x \right) = F_{37}\! \left(x \right) F_{4}\! \left(x \right)
F_{37}\! \left(x \right) = F_{38}\! \left(x \right)
F_{38}\! \left(x \right) = F_{15}\! \left(x \right)+F_{39}\! \left(x \right)+F_{49}\! \left(x \right)
F_{39}\! \left(x \right) = F_{4}\! \left(x \right) F_{40}\! \left(x \right)
F_{40}\! \left(x \right) = F_{41}\! \left(x \right)+F_{43}\! \left(x \right)
F_{41}\! \left(x \right) = F_{4}\! \left(x \right)+F_{42}\! \left(x \right)
F_{42}\! \left(x \right) = F_{16}\! \left(x \right)
F_{43}\! \left(x \right) = F_{38}\! \left(x \right)+F_{44}\! \left(x \right)
F_{44}\! \left(x \right) = 2 F_{15}\! \left(x \right)+F_{36}\! \left(x \right)+F_{45}\! \left(x \right)
F_{45}\! \left(x \right) = F_{4}\! \left(x \right) F_{46}\! \left(x \right)
F_{46}\! \left(x \right) = F_{47}\! \left(x \right)+F_{48}\! \left(x \right)
F_{47}\! \left(x \right) = F_{42}\! \left(x \right)
F_{48}\! \left(x \right) = F_{44}\! \left(x \right)
F_{49}\! \left(x \right) = F_{20}\! \left(x \right) F_{4}\! \left(x \right)
F_{50}\! \left(x \right) = F_{4}\! \left(x \right) F_{51}\! \left(x \right)
F_{51}\! \left(x \right) = F_{20}\! \left(x \right)+F_{38}\! \left(x \right)
F_{52}\! \left(x \right) = F_{137}\! \left(x \right)+F_{15}\! \left(x \right)+F_{53}\! \left(x \right)
F_{53}\! \left(x \right) = F_{4}\! \left(x \right) F_{54}\! \left(x \right)
F_{54}\! \left(x \right) = F_{55}\! \left(x \right)+F_{62}\! \left(x \right)
F_{55}\! \left(x \right) = F_{56}\! \left(x \right)+F_{7}\! \left(x \right)
F_{56}\! \left(x \right) = F_{15}\! \left(x \right)+F_{16}\! \left(x \right)+F_{57}\! \left(x \right)
F_{57}\! \left(x \right) = F_{4}\! \left(x \right) F_{58}\! \left(x \right)
F_{58}\! \left(x \right) = F_{11}\! \left(x \right)+F_{59}\! \left(x \right)
F_{59}\! \left(x \right) = F_{29}\! \left(x \right)+F_{60}\! \left(x \right)
F_{60}\! \left(x \right) = F_{61}\! \left(x \right)
F_{61}\! \left(x \right) = F_{29}\! \left(x \right) F_{4}\! \left(x \right)
F_{62}\! \left(x \right) = F_{52}\! \left(x \right)+F_{63}\! \left(x \right)
F_{63}\! \left(x \right) = F_{125}\! \left(x \right)+F_{15}\! \left(x \right)+F_{64}\! \left(x \right)+F_{90}\! \left(x \right)
F_{64}\! \left(x \right) = F_{4}\! \left(x \right) F_{65}\! \left(x \right)
F_{65}\! \left(x \right) = F_{66}\! \left(x \right)+F_{70}\! \left(x \right)
F_{66}\! \left(x \right) = F_{56}\! \left(x \right)+F_{67}\! \left(x \right)
F_{67}\! \left(x \right) = F_{68}\! \left(x \right)
F_{68}\! \left(x \right) = F_{4}\! \left(x \right) F_{69}\! \left(x \right)
F_{69}\! \left(x \right) = F_{59}\! \left(x \right)
F_{70}\! \left(x \right) = F_{63}\! \left(x \right)+F_{71}\! \left(x \right)
F_{71}\! \left(x \right) = 2 F_{15}\! \left(x \right)+F_{72}\! \left(x \right)+F_{76}\! \left(x \right)+F_{77}\! \left(x \right)
F_{72}\! \left(x \right) = F_{4}\! \left(x \right) F_{73}\! \left(x \right)
F_{73}\! \left(x \right) = F_{74}\! \left(x \right)+F_{75}\! \left(x \right)
F_{74}\! \left(x \right) = F_{67}\! \left(x \right)
F_{75}\! \left(x \right) = F_{71}\! \left(x \right)
F_{76}\! \left(x \right) = 0
F_{77}\! \left(x \right) = F_{4}\! \left(x \right) F_{78}\! \left(x \right)
F_{78}\! \left(x \right) = F_{79}\! \left(x \right)
F_{79}\! \left(x \right) = F_{80}\! \left(x \right)+F_{84}\! \left(x \right)
F_{80}\! \left(x \right) = F_{81}\! \left(x \right)
F_{81}\! \left(x \right) = F_{4}\! \left(x \right) F_{82}\! \left(x \right)
F_{82}\! \left(x \right) = F_{34}\! \left(x \right)+F_{83}\! \left(x \right)
F_{83}\! \left(x \right) = F_{80}\! \left(x \right)
F_{84}\! \left(x \right) = 3 F_{15}\! \left(x \right)+F_{85}\! \left(x \right)+F_{89}\! \left(x \right)
F_{85}\! \left(x \right) = F_{4}\! \left(x \right) F_{86}\! \left(x \right)
F_{86}\! \left(x \right) = F_{87}\! \left(x \right)+F_{88}\! \left(x \right)
F_{87}\! \left(x \right) = F_{60}\! \left(x \right)
F_{88}\! \left(x \right) = F_{84}\! \left(x \right)
F_{89}\! \left(x \right) = F_{4}\! \left(x \right) F_{80}\! \left(x \right)
F_{90}\! \left(x \right) = F_{4}\! \left(x \right) F_{91}\! \left(x \right)
F_{91}\! \left(x \right) = F_{92}\! \left(x \right)
F_{92}\! \left(x \right) = F_{15}\! \left(x \right)+F_{49}\! \left(x \right)+F_{93}\! \left(x \right)
F_{93}\! \left(x \right) = F_{4}\! \left(x \right) F_{94}\! \left(x \right)
F_{94}\! \left(x \right) = F_{95}\! \left(x \right)+F_{96}\! \left(x \right)
F_{95}\! \left(x \right) = F_{14}\! \left(x \right)+F_{4}\! \left(x \right)
F_{96}\! \left(x \right) = F_{92}\! \left(x \right)+F_{97}\! \left(x \right)
F_{97}\! \left(x \right) = F_{106}\! \left(x \right)+F_{15}\! \left(x \right)+F_{90}\! \left(x \right)+F_{98}\! \left(x \right)
F_{98}\! \left(x \right) = F_{4}\! \left(x \right) F_{99}\! \left(x \right)
F_{99}\! \left(x \right) = F_{100}\! \left(x \right)+F_{101}\! \left(x \right)
F_{100}\! \left(x \right) = F_{14}\! \left(x \right)+F_{60}\! \left(x \right)
F_{101}\! \left(x \right) = F_{102}\! \left(x \right)+F_{97}\! \left(x \right)
F_{102}\! \left(x \right) = 2 F_{15}\! \left(x \right)+F_{103}\! \left(x \right)+F_{76}\! \left(x \right)+F_{89}\! \left(x \right)
F_{103}\! \left(x \right) = F_{104}\! \left(x \right) F_{4}\! \left(x \right)
F_{104}\! \left(x \right) = F_{105}\! \left(x \right)+F_{87}\! \left(x \right)
F_{105}\! \left(x \right) = F_{102}\! \left(x \right)
F_{106}\! \left(x \right) = F_{107}\! \left(x \right) F_{4}\! \left(x \right)
F_{107}\! \left(x \right) = F_{108}\! \left(x \right)
F_{108}\! \left(x \right) = F_{109}\! \left(x \right) F_{4}\! \left(x \right)
F_{109}\! \left(x \right) = F_{110}\! \left(x \right)+F_{28}\! \left(x \right)
F_{110}\! \left(x \right) = F_{107}\! \left(x \right)+F_{111}\! \left(x \right)
F_{111}\! \left(x \right) = 2 F_{15}\! \left(x \right)+F_{112}\! \left(x \right)+F_{115}\! \left(x \right)
F_{112}\! \left(x \right) = F_{113}\! \left(x \right) F_{4}\! \left(x \right)
F_{113}\! \left(x \right) = F_{114}\! \left(x \right)+F_{34}\! \left(x \right)
F_{114}\! \left(x \right) = F_{111}\! \left(x \right)
F_{115}\! \left(x \right) = F_{116}\! \left(x \right) F_{4}\! \left(x \right)
F_{116}\! \left(x \right) = F_{117}\! \left(x \right)
F_{117}\! \left(x \right) = F_{118}\! \left(x \right)
F_{118}\! \left(x \right) = F_{119}\! \left(x \right) F_{4}\! \left(x \right)
F_{119}\! \left(x \right) = F_{120}\! \left(x \right)+F_{41}\! \left(x \right)
F_{120}\! \left(x \right) = F_{117}\! \left(x \right)+F_{121}\! \left(x \right)
F_{121}\! \left(x \right) = 2 F_{15}\! \left(x \right)+F_{115}\! \left(x \right)+F_{122}\! \left(x \right)
F_{122}\! \left(x \right) = F_{123}\! \left(x \right) F_{4}\! \left(x \right)
F_{123}\! \left(x \right) = F_{124}\! \left(x \right)+F_{47}\! \left(x \right)
F_{124}\! \left(x \right) = F_{121}\! \left(x \right)
F_{125}\! \left(x \right) = F_{126}\! \left(x \right) F_{4}\! \left(x \right)
F_{126}\! \left(x \right) = F_{127}\! \left(x \right)+F_{79}\! \left(x \right)
F_{127}\! \left(x \right) = F_{107}\! \left(x \right)+F_{128}\! \left(x \right)
F_{128}\! \left(x \right) = 2 F_{15}\! \left(x \right)+F_{106}\! \left(x \right)+F_{129}\! \left(x \right)
F_{129}\! \left(x \right) = F_{130}\! \left(x \right) F_{4}\! \left(x \right)
F_{130}\! \left(x \right) = F_{100}\! \left(x \right)+F_{131}\! \left(x \right)
F_{131}\! \left(x \right) = F_{128}\! \left(x \right)+F_{132}\! \left(x \right)
F_{132}\! \left(x \right) = 2 F_{15}\! \left(x \right)+F_{133}\! \left(x \right)+F_{136}\! \left(x \right)+F_{89}\! \left(x \right)
F_{133}\! \left(x \right) = F_{134}\! \left(x \right) F_{4}\! \left(x \right)
F_{134}\! \left(x \right) = F_{135}\! \left(x \right)+F_{87}\! \left(x \right)
F_{135}\! \left(x \right) = F_{132}\! \left(x \right)
F_{136}\! \left(x \right) = 0
F_{137}\! \left(x \right) = F_{138}\! \left(x \right) F_{4}\! \left(x \right)
F_{138}\! \left(x \right) = F_{127}\! \left(x \right)+F_{139}\! \left(x \right)
F_{139}\! \left(x \right) = F_{20}\! \left(x \right)+F_{92}\! \left(x \right)
System of equations in sympy syntax:
Eq(F_0(x), F_1(x) + F_2(x))
Eq(F_1(x), 1)
Eq(F_2(x), F_3(x))
Eq(F_3(x), F_4(x)*F_5(x))
Eq(F_4(x), x)
Eq(F_5(x), F_19(x) + F_6(x))
Eq(F_6(x), F_1(x) + F_7(x))
Eq(F_7(x), F_8(x))
Eq(F_8(x), F_4(x)*F_9(x))
Eq(F_9(x), F_10(x) + F_11(x))
Eq(F_10(x), F_1(x) + F_4(x))
Eq(F_11(x), F_12(x) + F_14(x))
Eq(F_12(x), F_13(x))
Eq(F_13(x), F_10(x)*F_4(x))
Eq(F_14(x), F_15(x) + F_16(x) + F_18(x))
Eq(F_15(x), 0)
Eq(F_16(x), F_17(x)*F_4(x))
Eq(F_17(x), F_4(x))
Eq(F_18(x), F_12(x)*F_4(x))
Eq(F_19(x), F_20(x) + F_52(x))
Eq(F_20(x), F_21(x))
Eq(F_21(x), F_22(x)*F_4(x))
Eq(F_22(x), F_23(x) + F_24(x))
Eq(F_23(x), F_1(x) + F_12(x))
Eq(F_24(x), F_20(x) + F_25(x))
Eq(F_25(x), F_15(x) + F_26(x) + F_50(x))
Eq(F_26(x), F_27(x)*F_4(x))
Eq(F_27(x), F_28(x) + F_30(x))
Eq(F_28(x), F_12(x) + F_29(x))
Eq(F_29(x), F_16(x))
Eq(F_30(x), F_25(x) + F_31(x))
Eq(F_31(x), 2*F_15(x) + F_32(x) + F_36(x))
Eq(F_32(x), F_33(x)*F_4(x))
Eq(F_33(x), F_34(x) + F_35(x))
Eq(F_34(x), F_29(x))
Eq(F_35(x), F_31(x))
Eq(F_36(x), F_37(x)*F_4(x))
Eq(F_37(x), F_38(x))
Eq(F_38(x), F_15(x) + F_39(x) + F_49(x))
Eq(F_39(x), F_4(x)*F_40(x))
Eq(F_40(x), F_41(x) + F_43(x))
Eq(F_41(x), F_4(x) + F_42(x))
Eq(F_42(x), F_16(x))
Eq(F_43(x), F_38(x) + F_44(x))
Eq(F_44(x), 2*F_15(x) + F_36(x) + F_45(x))
Eq(F_45(x), F_4(x)*F_46(x))
Eq(F_46(x), F_47(x) + F_48(x))
Eq(F_47(x), F_42(x))
Eq(F_48(x), F_44(x))
Eq(F_49(x), F_20(x)*F_4(x))
Eq(F_50(x), F_4(x)*F_51(x))
Eq(F_51(x), F_20(x) + F_38(x))
Eq(F_52(x), F_137(x) + F_15(x) + F_53(x))
Eq(F_53(x), F_4(x)*F_54(x))
Eq(F_54(x), F_55(x) + F_62(x))
Eq(F_55(x), F_56(x) + F_7(x))
Eq(F_56(x), F_15(x) + F_16(x) + F_57(x))
Eq(F_57(x), F_4(x)*F_58(x))
Eq(F_58(x), F_11(x) + F_59(x))
Eq(F_59(x), F_29(x) + F_60(x))
Eq(F_60(x), F_61(x))
Eq(F_61(x), F_29(x)*F_4(x))
Eq(F_62(x), F_52(x) + F_63(x))
Eq(F_63(x), F_125(x) + F_15(x) + F_64(x) + F_90(x))
Eq(F_64(x), F_4(x)*F_65(x))
Eq(F_65(x), F_66(x) + F_70(x))
Eq(F_66(x), F_56(x) + F_67(x))
Eq(F_67(x), F_68(x))
Eq(F_68(x), F_4(x)*F_69(x))
Eq(F_69(x), F_59(x))
Eq(F_70(x), F_63(x) + F_71(x))
Eq(F_71(x), 2*F_15(x) + F_72(x) + F_76(x) + F_77(x))
Eq(F_72(x), F_4(x)*F_73(x))
Eq(F_73(x), F_74(x) + F_75(x))
Eq(F_74(x), F_67(x))
Eq(F_75(x), F_71(x))
Eq(F_76(x), 0)
Eq(F_77(x), F_4(x)*F_78(x))
Eq(F_78(x), F_79(x))
Eq(F_79(x), F_80(x) + F_84(x))
Eq(F_80(x), F_81(x))
Eq(F_81(x), F_4(x)*F_82(x))
Eq(F_82(x), F_34(x) + F_83(x))
Eq(F_83(x), F_80(x))
Eq(F_84(x), 3*F_15(x) + F_85(x) + F_89(x))
Eq(F_85(x), F_4(x)*F_86(x))
Eq(F_86(x), F_87(x) + F_88(x))
Eq(F_87(x), F_60(x))
Eq(F_88(x), F_84(x))
Eq(F_89(x), F_4(x)*F_80(x))
Eq(F_90(x), F_4(x)*F_91(x))
Eq(F_91(x), F_92(x))
Eq(F_92(x), F_15(x) + F_49(x) + F_93(x))
Eq(F_93(x), F_4(x)*F_94(x))
Eq(F_94(x), F_95(x) + F_96(x))
Eq(F_95(x), F_14(x) + F_4(x))
Eq(F_96(x), F_92(x) + F_97(x))
Eq(F_97(x), F_106(x) + F_15(x) + F_90(x) + F_98(x))
Eq(F_98(x), F_4(x)*F_99(x))
Eq(F_99(x), F_100(x) + F_101(x))
Eq(F_100(x), F_14(x) + F_60(x))
Eq(F_101(x), F_102(x) + F_97(x))
Eq(F_102(x), F_103(x) + 2*F_15(x) + F_76(x) + F_89(x))
Eq(F_103(x), F_104(x)*F_4(x))
Eq(F_104(x), F_105(x) + F_87(x))
Eq(F_105(x), F_102(x))
Eq(F_106(x), F_107(x)*F_4(x))
Eq(F_107(x), F_108(x))
Eq(F_108(x), F_109(x)*F_4(x))
Eq(F_109(x), F_110(x) + F_28(x))
Eq(F_110(x), F_107(x) + F_111(x))
Eq(F_111(x), F_112(x) + F_115(x) + 2*F_15(x))
Eq(F_112(x), F_113(x)*F_4(x))
Eq(F_113(x), F_114(x) + F_34(x))
Eq(F_114(x), F_111(x))
Eq(F_115(x), F_116(x)*F_4(x))
Eq(F_116(x), F_117(x))
Eq(F_117(x), F_118(x))
Eq(F_118(x), F_119(x)*F_4(x))
Eq(F_119(x), F_120(x) + F_41(x))
Eq(F_120(x), F_117(x) + F_121(x))
Eq(F_121(x), F_115(x) + F_122(x) + 2*F_15(x))
Eq(F_122(x), F_123(x)*F_4(x))
Eq(F_123(x), F_124(x) + F_47(x))
Eq(F_124(x), F_121(x))
Eq(F_125(x), F_126(x)*F_4(x))
Eq(F_126(x), F_127(x) + F_79(x))
Eq(F_127(x), F_107(x) + F_128(x))
Eq(F_128(x), F_106(x) + F_129(x) + 2*F_15(x))
Eq(F_129(x), F_130(x)*F_4(x))
Eq(F_130(x), F_100(x) + F_131(x))
Eq(F_131(x), F_128(x) + F_132(x))
Eq(F_132(x), F_133(x) + F_136(x) + 2*F_15(x) + F_89(x))
Eq(F_133(x), F_134(x)*F_4(x))
Eq(F_134(x), F_135(x) + F_87(x))
Eq(F_135(x), F_132(x))
Eq(F_136(x), 0)
Eq(F_137(x), F_138(x)*F_4(x))
Eq(F_138(x), F_127(x) + F_139(x))
Eq(F_139(x), F_20(x) + F_92(x))
Pack JSON:
{"expansion_strats": [[{"class_module": "tilings.strategies.requirement_insertion", "extra_basis": [], "ignore_parent": false, "maxreqlen": 1, "one_cell_only": false, "strategy_class": "CellInsertionFactory"}, {"class_module": "tilings.strategies.requirement_placement", "dirs": [0, 1, 2, 3], "ignore_parent": false, "partial": false, "point_only": false, "strategy_class": "PatternPlacementFactory"}]], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "strategy_class": "RowColumnSeparationStrategy", "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "initial_strats": [{"class_module": "tilings.strategies.factor", "ignore_parent": true, "interleaving": null, "strategy_class": "FactorFactory", "tracked": false, "unions": false, "workable": true}], "iterative": false, "name": "point_placements", "symmetries": [], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "ignore_parent": false, "strategy_class": "InsertionEncodingVerificationStrategy"}, {"basis": [], "class_module": "tilings.strategies.verification", "ignore_parent": false, "strategy_class": "OneByOneVerificationStrategy", "symmetry": false}, {"basis": [], "class_module": "tilings.strategies.verification", "ignore_parent": false, "strategy_class": "LocallyFactorableVerificationStrategy", "symmetry": false}]}
Specification JSON:
{"root": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, "rules": [{"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_insertion", "gps": [{"patt": [0], "pos": [[0, 0]]}], "ignore_parent": true, "strategy_class": "RequirementInsertionStrategy"}}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [2, 1, 0], "pos": [[0, 1], [0, 1], [0, 0]]}, {"patt": [2, 1, 0], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 1]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 1], [0, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 1], [0, 1]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 0], [0, 1], [0, 0], [0, 0]]}], "requirements": []}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", 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